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October 2015 Estimation and inference in generalized additive coefficient models for nonlinear interactions with high-dimensional covariates
Shujie Ma, Raymond J. Carroll, Hua Liang, Shizhong Xu
Ann. Statist. 43(5): 2102-2131 (October 2015). DOI: 10.1214/15-AOS1344

Abstract

In the low-dimensional case, the generalized additive coefficient model (GACM) proposed by Xue and Yang [Statist. Sinica 16 (2006) 1423–1446] has been demonstrated to be a powerful tool for studying nonlinear interaction effects of variables. In this paper, we propose estimation and inference procedures for the GACM when the dimension of the variables is high. Specifically, we propose a groupwise penalization based procedure to distinguish significant covariates for the “large $p$ small $n$” setting. The procedure is shown to be consistent for model structure identification. Further, we construct simultaneous confidence bands for the coefficient functions in the selected model based on a refined two-step spline estimator. We also discuss how to choose the tuning parameters. To estimate the standard deviation of the functional estimator, we adopt the smoothed bootstrap method. We conduct simulation experiments to evaluate the numerical performance of the proposed methods and analyze an obesity data set from a genome-wide association study as an illustration.

Citation

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Shujie Ma. Raymond J. Carroll. Hua Liang. Shizhong Xu. "Estimation and inference in generalized additive coefficient models for nonlinear interactions with high-dimensional covariates." Ann. Statist. 43 (5) 2102 - 2131, October 2015. https://doi.org/10.1214/15-AOS1344

Information

Received: 1 September 2014; Revised: 1 May 2015; Published: October 2015
First available in Project Euclid: 3 August 2015

zbMATH: 1323.62033
MathSciNet: MR3375878
Digital Object Identifier: 10.1214/15-AOS1344

Subjects:
Primary: 62G08
Secondary: 62F12, 62G10, 62G20, 62J02

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 5 • October 2015
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